If the board doesn't recover from removing the CMOS battery for at least an hour (I would give it 24 hours), then you should inspect the board's electrolytic capacitors. Capacitors degrade with age and exposure to heat.

Look for bulging or leaking capacitors. The best way to check the capacitors is with an ESR meter, because not all defective capacitors have visual indications of being defective.

Do a Google search for testing capacitors with an ESR meter and recapping motherboards.